| Title:
|
Change-point estimator in gradually changing sequences (English) |
| Author:
|
Jarušková, Daniela |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
551-561 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Recently Hu\v{s}ková (1998) has studied the least squares estimator of a change-point in gradually changing sequence supposing that the sequence increases (or decreases) linearly after the change-point. The present paper shows that the limit behavior of the change-point estimator for more complicated gradual changes is similar. The limit variance of the estimator can be easily calculated from the covariance function of a limit process. (English) |
| Keyword:
|
gradual type of change |
| Keyword:
|
polynomial regression |
| Keyword:
|
estimator |
| Keyword:
|
limit distribution |
| MSC:
|
60F17 |
| MSC:
|
62E20 |
| MSC:
|
62G20 |
| idZBL:
|
Zbl 0962.62019 |
| idMR:
|
MR1666790 |
| . |
| Date available:
|
2009-01-08T18:46:17Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119032 |
| . |
| Reference:
|
[1] Anderson T.W.: The Statistical Analysis of Time Series.John Wiley New York (1971). Zbl 0225.62108, MR 0283939 |
| Reference:
|
[2] Billingsley P.: Convergence of Probability Measures.John Wiley New York (1968). Zbl 0172.21201, MR 0233396 |
| Reference:
|
[3] Davies R.B.: Hypothesis testing when a nuisance parameter is present only under the alternative.Biometrika 74 33-43 (1987). Zbl 0612.62023, MR 0885917 |
| Reference:
|
[4] Hinkley D.: Inference about the intersection in two-phase regression.Biometrika 56 495-504 (1969). Zbl 0183.48505 |
| Reference:
|
[5] Hušková M.: Estimation in location model with gradual changes.Comment. Math. Univ. Carolinae 39 (1998), 147-157. MR 1623002 |
| Reference:
|
[6] Knowles M., Siegmund D., Zhang H.: Confidence regions in semilinear regression.Biometrika 78 15-31 (1991). Zbl 0728.62063, MR 1118227 |
| Reference:
|
[7] Petrov V.V.: Predel'nyje teoremy dlja sum nezavisimych slucajnych velicin.Nauka Moskva (1987). MR 0896036 |
| Reference:
|
[8] Siegmund D., Zhang H.: Confidence region in broken line regression.Change-point problems IMS Lecture Notes - Monograph Series 23 292-316. MR 1477932 |
| . |
